Britain's 10-year government borrowing costs also sank below 1 percent for the first time ever.

Finance minister George Osborne said on Monday the economy would have to face up to "an adjustment" as it dealt with the fallout of "Brexit." Against a backdrop of sliding share prices and an uncertain economic outlook, investors sold sterling and sought the safety of government bonds.

Sterling shed more than 3 percent against the dollar to a fresh 31-year low of $1.3221, and the euro rose more than 2 percent to 83.25 pence, its highest in more than two years.

The pound's fall on Friday was the largest in modern history, reaching more than 10 percent against the dollar at one stage, and was also the largest decline since at least the 1970s on a trade-weighted basis.

Some, like Unicredit, reckon the pound will fall even further, perhaps as low as $1.20.

"The clear risk must be for further downside," said Neil Mellor, a currency strategist at Bank of New York Mellon in London. "Uncertainty equals currency weakness, we know this, and there is no sense that this (sterling) is a value trade right now and that you have to get back in. It is too early for anyone to start calling a bottom."

Analysts at RBC Capital Markets pointed to the history of past sell-offs as pointing the way towards $1.20-1.25 for the pound by the end of the third quarter of this year.